A first order convergent sequence of graphs can be associated with an analytic limit object,
which is referred to as a modeling limit (see Subsection REF  for a formal definition).
However, not every first order convergent sequence of graphs has a modeling limit [1]} and
establishing the existence of a modeling limit for first order convergent sequences of graphs
is an important problem in relation to first order convergence of graphs:
a modeling limit of a first order convergent sequence of dense graphs yields a graphon,
the standard limit object for convergent sequences of dense graphs, and
a modeling limit of a first order convergent sequence of sparse graphs that satisfies
the strong finitary mass transport principle (see Subsection REF  for the definition of the principle)
yields a graphing, the standard limit object for convergent sequence of sparse graphs.
